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ON THE RELATIVE LUSTERNIK–SCHNIRELMANN CATEGORY WITH RESPECT TO A REAL COHOMOLOGY CLASS
TIEQIANG LI, DIRK SCHÜTZ
Journal:

Glasgow Mathematical Journal / Volume 53 / Issue 1 / January 2011

Published online by Cambridge University Press:

25 August 2010, pp. 169-183

Print publication:

January 2011
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In this paper, we study a homotopy invariant cat(X, B, [ω]) on a pair (X, B) of finite CW complexes with respect to the cohomology class of a continuous closed 1-form ω. This is a generalisation of a Lusternik–Schnirelmann-category-type cat(X, [ω]), developed by Farber in [3, 4], studying the topology of a closed 1-form. This paper establishes the connection with the original notion cat(X, [ω]) and obtains analogous results on critical points and homoclinic cycles. We also provide a similar ‘cuplength’ lower bound for cat(X, B, [ω]).